Question 731797: Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given condition.
-1, -3, 0; f(-2) = -8
I have tried this:
(x+1)(x+3)(x+0)
=(x+0)(x^2+4x+3)
=x^3+4x^2+3x
then
f(-8)=a(-2+1)(-2+3)(-2+0)
=f(-8)=a(-1)(1)(-2)
-8=a-2
a=4
so then I combine the two, and I get:
4(x^3+4x^2+3x)
=4x^3+16x^2+12x
and I divide by 4x, I get:
4x(x^2+4x+3) and I simplify that to:
4x(x+1)(x+3)
but the answer is wrong. Any idea what I did wrong?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given condition.
-1, -3, 0; f(-2) = -8
I have tried this:
(x+1)(x+3)(x+0)
=(x+0)(x^2+4x+3)
=x^3+4x^2+3x
then
f(-8)=a(-2+1)(-2+3)(-2+0) ************ f(-2), not f(-8)
---------
f(-2) = -8 + 16 - 6 = 2
--------
--> (-3)*(x^3+4x^2+3x)
f(x) = -3x^3 - 12x^2 - 9x
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